Study the pattern:
$9\times 9=8199\times 99=9801999\times 999=998001$
Using the pattern, what is $9999\times 9999$?

The results are 81, 9801, 998001. The pattern for $n$ nines is $(n-1)$ nines, then 8, then $(n-1)$ zeros, then 1. For 4 nines: 999 80001 -> 99980001. Check: $9999^2=99980001$.